Stability of Flow Past Alternate Rigid and Porous Panels in Boundary Layer Flow and in Channel Flow

Propagation of two-dimensional small amplitude Tollmien-Schlichting (TS) waves has been investigated over a rigid panel followed by a porous panel in the presence of cross-flow. In the present work boundary layer flow over alternate rigid-porous panels in which suction is applied through the porous panel is investigated.Also investigated is the problem of flow past alternate rigid and porous panels with cross flow. A general space marching solution has been discussed for calculating the mean velocity profile for the above case, in the developing region of mean flow in the porous panel, following the rigid-porous junction. Numerical solutions are obtained using a finite difference method for the suitably simplified Navier Stokes equations, using appropriate boundary conditions.Detailed two-dimensional analyses have been done for the disturbance waves using both the quasi-parallel (QP) approximation, and more accurately, using the non-parallel (NP) approach. The non-parallel approach has been carried out over the developing mean-flow region of the porous panel, following the rigid-porous junction.Numerical solutions have been obtained by finite difference procedures. In some of the cases results have been validated with the available literature. Finally, the jumps in the amplitude of the disturbance waves across the rigid- porous junction were calculated using the theory of Sen et al.[6].The important outcome from this work is in optimizing the length of the porous panel, following the rigid-porous junction. It is seen that, as compared to the length required to approach the asymptotic mean flow state to within 99%, only a very short porous panel length is sufficient to stabilize the disturbances.Hence, it is foreseen that alternate long rigid panels, with in-between short porous panels, could be a very effective way of stabilizing the disturbances, and thus delaying laminar to turbulent transition.